By Ziad Saliba
The reason that Pi lies between the flying fields of a circumscribed polygon and an inscribed polygon is quite wide in essence, because a circle is a polygon with un countable sides. So when we have our circle with a radius of one, the area of the circle becomes Pi. With polygons inscribing and circumscribing the circle we can see that if we raise the number of sides the area will get closer and closer to Pi.
In the picture above we see a hexagon circumscribed and a circle inscribed into a hexagon. Pi is the area of the circle, composition the larger hexagon has an area slightly above then Pi and the smaller one slightly under. As we add sides we puzzle out each shape closer to having infinite sides, closer to a circle, and in turn bringing their areas closer together theoretically meeting at Pi.
To find the area of circumscribed n-sided polygon and the area of an inscribed n-sided polygon, we need to different formulas. The following diagrams head the methods I used to find both formulas, and in the snuff it diagram they are proved on a open square.
35.19615242365.39867% 31.29903810658.65033%
103.2491969623.42515% 102.9389262616.45107%
203.1676888060.83067% 203.0901699441.
63684%
303.1531270580.36715% 303.1186753620.72948%
403.1480682730.20613% 403.1286893010.41073%
503.1457333630.13180% 503.1333308390.26298%
603.1444667570.09149% 603.1358538980.18267%
703.1437036250.06719% 703.1373758120.13423%
803.1432085610.05144% 803.1383638290.10278%
903.1428692540.04064% 903.1390413180.08121%
1003.1426266040.03291% 1003.1395259760.06578%
one hundred ten3.14244710.02720% 1103.1398845970.05437%
1203.1423105880.02285% 1203. cxl1573750.04569%
1303.142204360.01947% 1303.1403696690.03893%
1403.1421200770.01679% 1403.1405381250.03357%
1503.1420520860.01462% 1503.140674030.02924%
1603.1419964430.01285%...If you want to get a full essay, order it on our website: Orderessay
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